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Mirrors > Home > MPE Home > Th. List > df-im | Structured version Visualization version GIF version |
Description: Define a function whose value is the imaginary part of a complex number. See imval 14827 for its value, imcli 14888 for its closure, and replim 14836 for its use in decomposing a complex number. (Contributed by NM, 9-May-1999.) |
Ref | Expression |
---|---|
df-im | ⊢ ℑ = (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cim 14818 | . 2 class ℑ | |
2 | vx | . . 3 setvar 𝑥 | |
3 | cc 10878 | . . 3 class ℂ | |
4 | 2 | cv 1538 | . . . . 5 class 𝑥 |
5 | ci 10882 | . . . . 5 class i | |
6 | cdiv 11641 | . . . . 5 class / | |
7 | 4, 5, 6 | co 7284 | . . . 4 class (𝑥 / i) |
8 | cre 14817 | . . . 4 class ℜ | |
9 | 7, 8 | cfv 6437 | . . 3 class (ℜ‘(𝑥 / i)) |
10 | 2, 3, 9 | cmpt 5158 | . 2 class (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i))) |
11 | 1, 10 | wceq 1539 | 1 wff ℑ = (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i))) |
Colors of variables: wff setvar class |
This definition is referenced by: imval 14827 imf 14833 cnre2csqima 31870 |
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